EUREKA by Alpheus Bingham and Dwayne Spradlin

“Scientific and technological advance do not occur at a constant rate and on all fronts simultaneously. They are sparked by something. The frontiers are moving in fits and starts. . . The salient difference been Archimedes’ 10,001st bath and his 10,000 was Hiero’s question, and no doubt Hiero’s enormous control over the consequences of the answer.

Hiero, the tyrant of Syracuse, had ordered an artisan to construct a crown for him. The tyrant had paid for the crown and supplied all the gold that was to be used. . . How was Hiero to know that the gold he delivered had not had a portion removed and the remainder mixed with lead to produce the expected weight. Hiero could verify the honesty of the artisan by measuring the volume of the crown.

For this, he took it to a local citizen skilled in the art of mathematics. Archimedes examined the crown acknowledged the beautiful workmanship, and then delivered the bad news: The crown was an irregularly shaped object and he could not deliver to Hiero an accurate volume measure.

That night, as he lowered himself into the tub, he noticed the water rising along the sides of his ‘regularly shaped’ bath receptacle. As Archimedes watched, he realized this was a method to effectively measure the volume of an irregularly shaped objected. Archimedes was so excited that he leapt from the tub, never bothering to dress, and ran naked through the streets of Syracuse shouting, ‘Eureka! Eureka. I have found it. I have found it.’

Hiero’s question acted as a boundary object, that enabled a boundary to be crossed. The circumstances of Hiero’s question produced a shift in time and space so that an event occurred at this particular point in time and space rather than at some other. Challenges, or well-formulated questions-asked, are the boundary objects that enable human progress to occur as it does, in fits and starts, and the effectiveness of that progress is often a function of the effectiveness of the challenge itself. As frequently remarked, ‘A problem well-stated is a problem half solved.’”